The relation between multilocus population genetics and social evolution theory

Evolution at multiple gene positions is complicated. Direct selection on one gene disturbs the evolutionary dynamics of associated genes. Recent years have seen the development of a multilocus methodology for modeling evolution at arbitrary numbers of gene positions with arbitrary dominance and epistatic relations, mode of inheritance, genetic linkage, and recombination. We show that the approach is conceptually analogous to social evolutionary methodology, which focuses on selection acting on associated individuals. In doing so, we (1) make explicit the links between the multilocus methodology and the foundations of social evolution theory, namely, Price's theorem and Hamilton's rule; (2) relate the multilocus approach to levels-of-selection and neighbor-modulated-fitness approaches in social evolution; (3) highlight the equivalence between genetical hitchhiking and kin selection; (4) demonstrate that the multilocus methodology allows for social evolutionary analyses involving coevolution of multiple traits and genetical associations between nonrelatives, including individuals of different species; (5) show that this methodology helps solve problems of dynamic sufficiency in social evolution theory; (6) form links between invasion criteria in multilocus systems and Hamilton's rule of kin selection; (7) illustrate the generality and exactness of Hamilton's rule, which has previously been described as an approximate, heuristic result.     

Neutral theory in macroecology and population genetics

Current neutral theory in macroecology has many parallels with neutral theory in population genetics, but it also has many distinct features that arise because it focuses mainly on questions at the community level rather than at the population level. Here we highlight the similarities and differences between these two bodies of theories from the aspects of the operational units, definitions of neutrality, basic parameters, driving forces, spatial structure and community assembly rules. Compared with neutral theory in population genetics, whose development spans more than 40 years, neutral theory in ecology, which is only a few years old, is still immature and under-developed. There are many opportunities for major theoretical contributions, some of which can be adopted directly from population genetics, while others will require new theoretical work. We critically discuss these opportunities and theoretical challenges in neutral macroecology, particularly in regard to effective community size, ecological drift, community differentiation and ecological dominance.     

Stochastic theory of population genetics

Stochastic models of population genetics are studied with special reference to the biological interest. Mathematical methods are described for treating some simple models and their modifications aimed at the problems of the molecular evolution. Unified theory for treating different quantities is extensively developed and applied to some typical problems of current interest in genetics. Mathematical methods for treating geographically structured populations are given. Approximation formulae and their accuracy are discussed. Some criteria are given for a structured population to behave almost like a panmictic population of the same total size. Some quantities are shown to be independent of the geographical structure and their dynamics are described.     

Quasispecies theory in the context of population genetics

Background  

A number of recent papers have cast doubt on the applicability of the quasispecies concept to virus evolution, and have argued that population genetics is a more appropriate framework to describe virus evolution than quasispecies theory.     

Some one-dimensional migration models in population genetics theory

This paper gives a method for calculating the covariance of gene frequencies at any two points of a habitat which is a finite 1-dimensional interval. Selectively neutral genes are considered migrating according to a continuous parameter analogue of the stepping stone model. The method is to solve a partial differential equation for the covariance, together with boundary conditions of zero normal derivative (or reflecting barrier) type.     

Social structure and indirect genetic effects: genetics of social behaviour

The social environment modulates gene expression, physiology, behaviour and patterns of inheritance. For more than 50 years, this concept has been investigated using approaches that include partitioning the social component out of behavioural heritability estimates, studying maternal effects on offspring, and analysing dominance hierarchies. Recent advances have formalized this ‘social environment effect’ by providing a more nuanced approach to the study of social influences on behaviour while recognizing evolutionary implications. Yet, in most of these formulations, the dynamics of social interactions are not accounted for. Also, the reciprocity between individual behaviour and group‐level interactions has been largely ignored. Consistent with evolutionary theory, the principles of social interaction are conserved across a broad range of taxa. While noting parallels in diverse organisms, this review uses Drosophila melanogaster as a case study to revisit what is known about social interaction paradigms. We highlight the benefits of integrating the history and pattern of interactions among individuals for dissecting molecular mechanisms that underlie social modulation of behaviour.     

Sam Karlin and the stochastic theory of evolutionary population genetics

Sam Karlin’s role in the development of the stochastic theory of evolutionary population genetics is outlined, together with his work in developing BLAST theory.     

The lattice models of neutral multi-alleles in population genetics theory

The aim of this article is to study lattice models of neutral multi-alleles including Ohta-Kimura's step-wise mutation model. We shall show an outline of the construction of a unique strongly continuous non-negative semi-group associated with the infinite dimensional generator and show a general and straightforward method of obtaining the time dependent and equilibrium solutions of all polynomial moments of the gene frequencies. We shall discuss the spectrum of the diffusion processes and as an application we obtain all higher moments of the homozygosity.     

Mathematical models in genetics

In this study, we present some of the basic ideas of population genetics. The founders of population genetics are R.A. Fisher, S. Wright, and J. B.S. Haldane. They, not only developed almost all the basic theory associated with genetics, but they also initiated multiple experiments in support of their theories. One of the first significant insights, which are a result of the Hardy–Weinberg law, is Mendelian inheritance preserves genetic variation on which the natural selection acts. We will limit to simple models formulated in terms of differential equations. Some of those differential equations are nonlinear and thus emphasize issues such as the stability of the fixed points and time scales on which those equations operate. First, we consider the classic case when selection acts on diploid locus at which wу can get arbitrary number of alleles. Then, we consider summaries that include recombination and selection at multiple loci. Also, we discuss the evolution of quantitative traits. In this case, the theory is formulated in respect of directly measurable quantities. Special cases of this theory have been successfully used for many decades in plants and animals breeding.     

Host genetics and population structure effects on parasitic disease

Host genetic factors exert significant influences on differential susceptibility to many infectious diseases. In addition, population structure of both host and parasite may influence disease distribution patterns. In this study, we assess the effects of population structure on infectious disease in two populations in which host genetic factors influencing susceptibility to parasitic disease have been extensively studied. The first population is the Jirel population of eastern Nepal that has been the subject of research on the determinants of differential susceptibility to soil-transmitted helminth infections. The second group is a Brazilian population residing in an area endemic for Trypanosoma cruzi infection that has been assessed for genetic influences on differential disease progression in Chagas disease. For measures of Ascaris worm burden, within-population host genetic effects are generally more important than host population structure factors in determining patterns of infectious disease. No significant influences of population structure on measures associated with progression of cardiac disease in individuals who were seropositive for T. cruzi infection were found.     

Understanding population structure and historical demography in a conservation context: population genetics of an endangered fern

The construction of the world's largest hydroelectric scheme across the Yangtze River, the Three Gorges Dams (TGD), in the centre of a southern-central Chinese biodiversity hot spot, the Three Gorges Reservoir Area (TGRA), has attracted international concern and conservation action. To examine whether landscape changes to date have impacted regional flora, and to establish long-term monitoring baselines, we assessed the distribution and dynamics of an endangered and TGRA endemic fern, Adiantum reniforme var. sinense . For eight nuclear microsatellites, high levels of genetic diversity ( H _E = 0.653–0.781) and slightly elevated inbreeding ( F _IS = 0.077–0.197) were found across 13 surveyed populations. The population history of this fern is characterized by a balance of gene flow and genetic drift, where historical dispersal, inferred from coalescent ( F =  0.129) and genetic differentiation ( F _ST = 0.094 and R _ST = 0.180) approaches, is moderate, reflecting an isolation by distance relationship. Importantly, most populations exhibited mutation-drift disequilibrium, suggesting a recent population decline, which is congruent with the known demographic history of the species following dam-related activities. Based on these results, populations of A. reniforme var. sinense are expected to lose genetic diversity and increase genetic structure as dam-related activities decrease size and increase genetic isolation of remnants.     

Darwinian adaptation,population genetics and the streetcar theory of evolution

 This paper investigates the problem of how to conceive a robust theory of phenotypic adaptation in non-trivial models of evolutionary biology. A particular effort is made to develop a foundation of this theory in the context of n-locus population genetics. Therefore, the evolution of phenotypic traits is considered that are coded for by more than one gene. The potential for epistatic gene interactions is not a priori excluded. Furthermore, emphasis is laid on the intricacies of frequency-dependent selection. It is first discussed how strongly the scope for phenotypic adaptation is restricted by the complex nature of ‘reproduction mechanics’ in sexually reproducing diploid populations. This discussion shows that one can easily lose the traces of Darwinism in n-locus models of population genetics. In order to retrieve these traces, the outline of a new theory is given that I call ‘streetcar theory of evolution’. This theory is based on the same models that geneticists have used in order to demonstrate substantial problems with the ‘adaptationist programme’. However, these models are now analyzed differently by including thoughts about the evolutionary removal of genetic constraints. This requires consideration of a sufficiently wide range of potential mutant alleles and careful examination of what to consider as a stable state of the evolutionary process. A particular notion of stability is introduced in order to describe population states that are phenotypically stable against the effects of all mutant alleles that are to be expected in the long-run. Surprisingly, a long-term stable state can be characterized at the phenotypic level as a fitness maximum, a Nash equilibrium or an ESS. The paper presents these mathematical results and discusses – at unusual length for a mathematical journal – their fundamental role in our current understanding of evolution. Received 22 April 1994; received in revised form 10 July 1995